naginterfaces.library.wav.dim1_​mxolap_​multi_​inv

naginterfaces.library.wav.dim1_mxolap_multi_inv(nwlinv, keepa, c, n, comm)

dim1_mxolap_multi_inv computes the inverse one-dimensional multi-level maximal overlap discrete wavelet transform (MODWT). This function reconstructs data from (possibly filtered or otherwise manipulated) wavelet transform coefficients calculated by dim1_mxolap_multi_fwd() from an original set of data. The initialization function dim1_init() must be called first to set up the MODWT options.

For full information please refer to the NAG Library document for c09dd

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/c09/c09ddf.html

Parameters

nwlinvint

The number of levels to be used in the inverse multi-level transform. The number of levels must be less than or equal to $n_{fwd}$, which has the value of argument $\text{nwl}$ as used in the computation of the wavelet coefficients using dim1_mxolap_multi_fwd(). The data will be reconstructed to level $(\text{nwl}-nwlinv)$, where level $0$ is the original input dataset provided to dim1_mxolap_multi_fwd().

keepastr, length 1

Determines whether the approximation coefficients are stored in array $c$ for every level of the computed transform or else only for the final level. In both cases, the detail coefficients are stored in $c$ for every level computed.

$keepa=\text{‘A'}$

Retain approximation coefficients for all levels computed.

$keepa=\text{‘F'}$

Retain approximation coefficients for only the final level computed.

cfloat, array-like, shape $\left(\text{lenc}\right)$

The coefficients of a multi-level wavelet transform of the dataset.

The coefficients are stored in $c$ as follows:

If $keepa=\text{‘F'}$,

$c[0:n_a]$

Contains the level $n_l$ approximation coefficients;

$c[n_a+(i-1)\times n_d+1-1:n_a+i\times n_d]$

Contains the level $(n_l-\text{i}+1)$ detail coefficients, for $\text{i}=1,2,\dots ,n_l$;

If $keepa=\text{‘A'}$,

$c[(i-1)\times n_a:i\times n_a]$

Contains the level $(n_l-\text{i}+1)$ approximation coefficients, for $\text{i}=1,2,\dots ,n_l$;

$c[n_l\times n_a+(i-1)\times n_d:n_l\times n_a+i\times n_d]$

Contains the level $\text{i}$ detail coefficients, for $\text{i}=1,2,\dots ,n_l$.

The values $n_a$ and $n_d$ denote the numbers of approximation and detail coefficients respectively, which are equal.

This number is returned as output in $\text{na}$ from a preceding call to dim1_mxolap_multi_fwd().

See dim1_mxolap_multi_fwd() for details.

nint

$n$, the length of the data array, $y$, to be reconstructed.

commdict, communication object

Communication structure.

This argument must have been initialized by a prior call to dim1_init().

Returns

yfloat, ndarray, shape $\left(n\right)$

The dataset reconstructed from the multi-level wavelet transform coefficients and the transformation options supplied to the initialization function dim1_init().

Raises

NagValueError

(errno $1$)

On entry, $nwlinv$ is larger than the number of levels computed by the preceding call to dim1_mxolap_multi_fwd(): $nwlinv=⟨value⟩$, expected $⟨value⟩$.

(errno $1$)

On entry, $nwlinv=⟨value⟩$.

Constraint: $nwlinv\ge 1$.

(errno $3$)

On entry, $\text{lenc}$ is set too small: $\text{lenc}=⟨value⟩$.

Constraint: $\text{lenc}\ge ⟨value⟩$.

(errno $5$)

On entry, $n$ is inconsistent with the value passed to the initialization function: $n=⟨value⟩$, $n$ should be $⟨value⟩$.

(errno $7$)

On entry, the initialization function dim1_init() has not been called first or it has not been called with $wtrans=\text{‘U'}$, or the communication array $comm$[‘icomm’] has become corrupted.

(errno $21$)

On entry, $keepa=⟨value⟩$.

Constraint: $keepa=\text{‘F'}\text{or}\text{‘A'}$.

Notes

dim1_mxolap_multi_inv performs the inverse operation of dim1_mxolap_multi_fwd(). That is, given a set of wavelet coefficients computed by dim1_mxolap_multi_fwd() using a MODWT as set up by the initialization function dim1_init() on a real array of length $n$, dim1_mxolap_multi_inv will reconstruct the data array $y_{\text{i}}$, for $\text{i}=1,2,\dots ,n$, from which the coefficients were derived.

References

Percival, D B and Walden, A T, 2000, Wavelet Methods for Time Series Analysis, Cambridge University Press